Simplify the following expression: $ q = \dfrac{z + 1}{-2} + \dfrac{7}{4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{z + 1}{-2} \times \dfrac{4}{4} = \dfrac{4z + 4}{-8} $ Multiply the second expression by $\dfrac{-2}{-2}$ $ \dfrac{7}{4} \times \dfrac{-2}{-2} = \dfrac{-14}{-8} $ Therefore $ q = \dfrac{4z + 4}{-8} + \dfrac{-14}{-8} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{4z + 4 - 14}{-8} $ $q = \dfrac{4z - 10}{-8}$ Simplify the expression by dividing the numerator and denominator by -2: $q = \dfrac{-2z + 5}{4}$